As clear from the expression (REF ), the residue at a given pole \(s=m_k^2\)  is a polynomial in \(t\)  of degree \(k\) , corresponding to particle exchanges of spin \(j=0,\dots ,k\) . Note that the poles of our amplitude \(s=m^2+[k]_q\)  start from \(k=0\) , as opposed to [1]} where the poles (\(s=k\) ) start from \(k=-1\) . Thus we need to set \(m^2 =-1\)  and shift \(k\rightarrow (k+1)\)  in the expressions of \(a^q_{k,j}\)  to compare our results to [1]}. In our convention, the leading Regge trajectory is associated with coefficients of the form \(a^q_{k,k}\) .
